5444 lines
207 KiB
Plaintext
5444 lines
207 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "502c118b",
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"metadata": {
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"origin_pos": 0
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},
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"source": [
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"# 小批量随机梯度下降\n",
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":label:`sec_minibatch_sgd`\n",
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"\n",
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"到目前为止，我们在基于梯度的学习方法中遇到了两个极端情况：\n",
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" :numref:`sec_gd`中使用完整数据集来计算梯度并更新参数，\n",
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" :numref:`sec_sgd`中一次处理一个训练样本来取得进展。\n",
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"二者各有利弊：每当数据非常相似时，梯度下降并不是非常“数据高效”。\n",
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"而由于CPU和GPU无法充分利用向量化，随机梯度下降并不特别“计算高效”。\n",
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"这暗示了两者之间可能有折中方案，这便涉及到*小批量随机梯度下降*（minibatch gradient descent）。\n",
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"\n",
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"## 向量化和缓存\n",
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"\n",
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"使用小批量的决策的核心是计算效率。\n",
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"当考虑与多个GPU和多台服务器并行处理时，这一点最容易被理解。在这种情况下，我们需要向每个GPU发送至少一张图像。\n",
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"有了每台服务器8个GPU和16台服务器，我们就能得到大小为128的小批量。\n",
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"\n",
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"当涉及到单个GPU甚至CPU时，事情会更微妙一些：\n",
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"这些设备有多种类型的内存、通常情况下多种类型的计算单元以及在它们之间不同的带宽限制。\n",
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"例如，一个CPU有少量寄存器（register），L1和L2缓存，以及L3缓存（在不同的处理器内核之间共享）。\n",
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"随着缓存的大小的增加，它们的延迟也在增加，同时带宽在减少。\n",
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"可以说，处理器能够执行的操作远比主内存接口所能提供的多得多。\n",
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"\n",
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"首先，具有16个内核和AVX-512向量化的2GHz CPU每秒可处理高达$2 \\cdot 10^9 \\cdot 16 \\cdot 32 = 10^{12}$个字节。\n",
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"同时，GPU的性能很容易超过该数字100倍。\n",
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"而另一方面，中端服务器处理器的带宽可能不超过100Gb/s，即不到处理器满负荷所需的十分之一。\n",
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"更糟糕的是，并非所有的内存入口都是相等的：内存接口通常为64位或更宽（例如，在最多384位的GPU上）。\n",
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"因此读取单个字节会导致由于更宽的存取而产生的代价。\n",
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"\n",
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"其次，第一次存取的额外开销很大，而按序存取（sequential access）或突发读取（burst read）相对开销较小。\n",
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"有关更深入的讨论，请参阅此[维基百科文章](https://en.wikipedia.org/wiki/Cache_hierarchy)。\n",
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"\n",
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"减轻这些限制的方法是使用足够快的CPU缓存层次结构来为处理器提供数据。\n",
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"这是深度学习中批量处理背后的推动力。\n",
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"举一个简单的例子：矩阵-矩阵乘法。\n",
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"比如$\\mathbf{A} = \\mathbf{B}\\mathbf{C}$，我们有很多方法来计算$\\mathbf{A}$。例如，我们可以尝试以下方法：\n",
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"\n",
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"1. 我们可以计算$\\mathbf{A}_{ij} = \\mathbf{B}_{i,:} \\mathbf{C}_{:,j}^\\top$，也就是说，我们可以通过点积进行逐元素计算。\n",
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"1. 我们可以计算$\\mathbf{A}_{:,j} = \\mathbf{B} \\mathbf{C}_{:,j}^\\top$，也就是说，我们可以一次计算一列。同样，我们可以一次计算$\\mathbf{A}$一行$\\mathbf{A}_{i,:}$。\n",
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"1. 我们可以简单地计算$\\mathbf{A} = \\mathbf{B} \\mathbf{C}$。\n",
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"1. 我们可以将$\\mathbf{B}$和$\\mathbf{C}$分成较小的区块矩阵，然后一次计算$\\mathbf{A}$的一个区块。\n",
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"\n",
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"如果我们使用第一个选择，每次我们计算一个元素$\\mathbf{A}_{ij}$时，都需要将一行和一列向量复制到CPU中。\n",
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"更糟糕的是，由于矩阵元素是按顺序对齐的，因此当从内存中读取它们时，我们需要访问两个向量中许多不相交的位置。\n",
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"第二种选择相对更有利：我们能够在遍历$\\mathbf{B}$的同时，将列向量$\\mathbf{C}_{:,j}$保留在CPU缓存中。\n",
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"它将内存带宽需求减半，相应地提高了访问速度。\n",
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"第三种选择表面上是最可取的，然而大多数矩阵可能不能完全放入缓存中。\n",
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"第四种选择提供了一个实践上很有用的方案：我们可以将矩阵的区块移到缓存中然后在本地将它们相乘。\n",
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"让我们来看看这些操作在实践中的效率如何。\n",
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"\n",
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"除了计算效率之外，Python和深度学习框架本身带来的额外开销也是相当大的。\n",
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"回想一下，每次我们执行代码时，Python解释器都会向深度学习框架发送一个命令，要求将其插入到计算图中并在调度过程中处理它。\n",
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"这样的额外开销可能是非常不利的。\n",
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"总而言之，我们最好用向量化（和矩阵）。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "74d0b8bd",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:00:50.345234Z",
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"iopub.status.busy": "2023-08-18T07:00:50.344241Z",
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"iopub.status.idle": "2023-08-18T07:00:52.828095Z",
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"shell.execute_reply": "2023-08-18T07:00:52.826894Z"
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},
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"origin_pos": 2,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import torch\n",
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"from torch import nn\n",
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"from d2l import torch as d2l\n",
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"\n",
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"timer = d2l.Timer()\n",
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"A = torch.zeros(256, 256)\n",
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"B = torch.randn(256, 256)\n",
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"C = torch.randn(256, 256)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d11f4087",
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"metadata": {
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"origin_pos": 5
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},
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"source": [
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"按元素分配只需遍历分别为$\\mathbf{B}$和$\\mathbf{C}$的所有行和列，即可将该值分配给$\\mathbf{A}$。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "cf7f7a46",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:00:52.834373Z",
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"iopub.status.busy": "2023-08-18T07:00:52.833156Z",
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"iopub.status.idle": "2023-08-18T07:00:54.504095Z",
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"shell.execute_reply": "2023-08-18T07:00:54.502961Z"
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},
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"origin_pos": 7,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1.6609790325164795"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# 逐元素计算A=BC\n",
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"timer.start()\n",
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"for i in range(256):\n",
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" for j in range(256):\n",
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" A[i, j] = torch.dot(B[i, :], C[:, j])\n",
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"timer.stop()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a28f6b4d",
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"metadata": {
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"origin_pos": 10
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},
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"source": [
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"更快的策略是执行按列分配。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "312257cf",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:00:54.509396Z",
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"iopub.status.busy": "2023-08-18T07:00:54.508607Z",
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"iopub.status.idle": "2023-08-18T07:00:54.539525Z",
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"shell.execute_reply": "2023-08-18T07:00:54.537980Z"
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},
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"origin_pos": 12,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0.022588253021240234"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# 逐列计算A=BC\n",
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"timer.start()\n",
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"for j in range(256):\n",
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" A[:, j] = torch.mv(B, C[:, j])\n",
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"timer.stop()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "afb99637",
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"metadata": {
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"origin_pos": 15
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},
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"source": [
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"最有效的方法是在一个区块中执行整个操作。让我们看看它们各自的操作速度是多少。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "5735b43b",
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"metadata": {
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"execution": {
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|
"iopub.execute_input": "2023-08-18T07:00:54.544547Z",
|
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"iopub.status.busy": "2023-08-18T07:00:54.543948Z",
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"iopub.status.idle": "2023-08-18T07:00:54.561974Z",
|
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"shell.execute_reply": "2023-08-18T07:00:54.560964Z"
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},
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"origin_pos": 17,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"performance in Gigaflops: element 1.204, column 88.542, full 195.625\n"
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]
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}
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],
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"source": [
|
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"# 一次性计算A=BC\n",
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"timer.start()\n",
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"A = torch.mm(B, C)\n",
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"timer.stop()\n",
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"\n",
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"# 乘法和加法作为单独的操作（在实践中融合）\n",
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"gigaflops = [2/i for i in timer.times]\n",
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"print(f'performance in Gigaflops: element {gigaflops[0]:.3f}, '\n",
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" f'column {gigaflops[1]:.3f}, full {gigaflops[2]:.3f}')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d94851f8",
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"metadata": {
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"origin_pos": 20
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},
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"source": [
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"## 小批量\n",
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"\n",
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":label:`sec_minibatches`\n",
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"\n",
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"之前我们会理所当然地读取数据的*小批量*，而不是观测单个数据来更新参数，现在简要解释一下原因。\n",
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"处理单个观测值需要我们执行许多单一矩阵-矢量（甚至矢量-矢量）乘法，这耗费相当大，而且对应深度学习框架也要巨大的开销。\n",
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"这既适用于计算梯度以更新参数时，也适用于用神经网络预测。\n",
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"也就是说，每当我们执行$\\mathbf{w} \\leftarrow \\mathbf{w} - \\eta_t \\mathbf{g}_t$时，消耗巨大。其中\n",
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"\n",
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"$$\\mathbf{g}_t = \\partial_{\\mathbf{w}} f(\\mathbf{x}_{t}, \\mathbf{w}).$$\n",
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"\n",
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"我们可以通过将其应用于一个小批量观测值来提高此操作的*计算*效率。\n",
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"也就是说，我们将梯度$\\mathbf{g}_t$替换为一个小批量而不是单个观测值\n",
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"\n",
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"$$\\mathbf{g}_t = \\partial_{\\mathbf{w}} \\frac{1}{|\\mathcal{B}_t|} \\sum_{i \\in \\mathcal{B}_t} f(\\mathbf{x}_{i}, \\mathbf{w}).$$\n",
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"\n",
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"让我们看看这对$\\mathbf{g}_t$的统计属性有什么影响：由于$\\mathbf{x}_t$和小批量$\\mathcal{B}_t$的所有元素都是从训练集中随机抽出的，因此梯度的期望保持不变。\n",
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"另一方面，方差显著降低。\n",
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"由于小批量梯度由正在被平均计算的$b := |\\mathcal{B}_t|$个独立梯度组成，其标准差降低了$b^{-\\frac{1}{2}}$。\n",
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"这本身就是一件好事，因为这意味着更新与完整的梯度更接近了。\n",
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"\n",
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"直观来说，这表明选择大型的小批量$\\mathcal{B}_t$将是普遍可行的。\n",
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"然而，经过一段时间后，与计算代价的线性增长相比，标准差的额外减少是微乎其微的。\n",
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"在实践中我们选择一个足够大的小批量，它可以提供良好的计算效率同时仍适合GPU的内存。\n",
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"下面，我们来看看这些高效的代码。\n",
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"在里面我们执行相同的矩阵-矩阵乘法，但是这次我们将其一次性分为64列的“小批量”。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "1abe0207",
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"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:00:54.568121Z",
|
|
"iopub.status.busy": "2023-08-18T07:00:54.567048Z",
|
|
"iopub.status.idle": "2023-08-18T07:00:54.575140Z",
|
|
"shell.execute_reply": "2023-08-18T07:00:54.573950Z"
|
|
},
|
|
"origin_pos": 22,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
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"performance in Gigaflops: block 2056.535\n"
|
|
]
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|
}
|
|
],
|
|
"source": [
|
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"timer.start()\n",
|
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"for j in range(0, 256, 64):\n",
|
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" A[:, j:j+64] = torch.mm(B, C[:, j:j+64])\n",
|
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"timer.stop()\n",
|
|
"print(f'performance in Gigaflops: block {2 / timer.times[3]:.3f}')"
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]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "350a97c4",
|
|
"metadata": {
|
|
"origin_pos": 25
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|
},
|
|
"source": [
|
|
"显而易见，小批量上的计算基本上与完整矩阵一样有效。\n",
|
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"需要注意的是，在 :numref:`sec_batch_norm`中，我们使用了一种在很大程度上取决于小批量中的方差的正则化。\n",
|
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"随着后者增加，方差会减少，随之而来的是批量规范化带来的噪声注入的好处。\n",
|
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"关于实例，请参阅 :cite:`Ioffe.2017`，了解有关如何重新缩放并计算适当项目。\n",
|
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"\n",
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"## 读取数据集\n",
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"\n",
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"让我们来看看如何从数据中有效地生成小批量。\n",
|
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"下面我们使用NASA开发的测试机翼的数据集[不同飞行器产生的噪声](https://archive.ics.uci.edu/ml/datasets/Airfoil+Self-Noise)来比较这些优化算法。\n",
|
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"为方便起见，我们只使用前$1,500$样本。\n",
|
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"数据已作预处理：我们移除了均值并将方差重新缩放到每个坐标为$1$。\n"
|
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]
|
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},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "2965fbc9",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:00:54.580353Z",
|
|
"iopub.status.busy": "2023-08-18T07:00:54.579977Z",
|
|
"iopub.status.idle": "2023-08-18T07:00:54.587997Z",
|
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"shell.execute_reply": "2023-08-18T07:00:54.586803Z"
|
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},
|
|
"origin_pos": 27,
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"tab": [
|
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"pytorch"
|
|
]
|
|
},
|
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"outputs": [],
|
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"source": [
|
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"#@save\n",
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"d2l.DATA_HUB['airfoil'] = (d2l.DATA_URL + 'airfoil_self_noise.dat',\n",
|
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" '76e5be1548fd8222e5074cf0faae75edff8cf93f')\n",
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"\n",
|
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"#@save\n",
|
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"def get_data_ch11(batch_size=10, n=1500):\n",
|
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" data = np.genfromtxt(d2l.download('airfoil'),\n",
|
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" dtype=np.float32, delimiter='\\t')\n",
|
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" data = torch.from_numpy((data - data.mean(axis=0)) / data.std(axis=0))\n",
|
|
" data_iter = d2l.load_array((data[:n, :-1], data[:n, -1]),\n",
|
|
" batch_size, is_train=True)\n",
|
|
" return data_iter, data.shape[1]-1"
|
|
]
|
|
},
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|
{
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|
"cell_type": "markdown",
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"id": "cfec2ad4",
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"metadata": {
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"origin_pos": 30
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},
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"source": [
|
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"## 从零开始实现\n",
|
|
"\n",
|
|
" :numref:`sec_linear_scratch`一节中已经实现过小批量随机梯度下降算法。\n",
|
|
"我们在这里将它的输入参数变得更加通用，主要是为了方便本章后面介绍的其他优化算法也可以使用同样的输入。\n",
|
|
"具体来说，我们添加了一个状态输入`states`并将超参数放在字典`hyperparams`中。\n",
|
|
"此外，我们将在训练函数里对各个小批量样本的损失求平均，因此优化算法中的梯度不需要除以批量大小。\n"
|
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]
|
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},
|
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{
|
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"cell_type": "code",
|
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"execution_count": 7,
|
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"id": "f1624e05",
|
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"metadata": {
|
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"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:00:54.595789Z",
|
|
"iopub.status.busy": "2023-08-18T07:00:54.595436Z",
|
|
"iopub.status.idle": "2023-08-18T07:00:54.604397Z",
|
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"shell.execute_reply": "2023-08-18T07:00:54.603217Z"
|
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},
|
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"origin_pos": 32,
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"tab": [
|
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"pytorch"
|
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]
|
|
},
|
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"outputs": [],
|
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"source": [
|
|
"def sgd(params, states, hyperparams):\n",
|
|
" for p in params:\n",
|
|
" p.data.sub_(hyperparams['lr'] * p.grad)\n",
|
|
" p.grad.data.zero_()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2b4c7291",
|
|
"metadata": {
|
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"origin_pos": 35
|
|
},
|
|
"source": [
|
|
"下面实现一个通用的训练函数，以方便本章后面介绍的其他优化算法使用。\n",
|
|
"它初始化了一个线性回归模型，然后可以使用小批量随机梯度下降以及后续小节介绍的其他算法来训练模型。\n"
|
|
]
|
|
},
|
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{
|
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"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "72ee9f70",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:00:54.610003Z",
|
|
"iopub.status.busy": "2023-08-18T07:00:54.609641Z",
|
|
"iopub.status.idle": "2023-08-18T07:00:54.631566Z",
|
|
"shell.execute_reply": "2023-08-18T07:00:54.630601Z"
|
|
},
|
|
"origin_pos": 37,
|
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"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"#@save\n",
|
|
"def train_ch11(trainer_fn, states, hyperparams, data_iter,\n",
|
|
" feature_dim, num_epochs=2):\n",
|
|
" # 初始化模型\n",
|
|
" w = torch.normal(mean=0.0, std=0.01, size=(feature_dim, 1),\n",
|
|
" requires_grad=True)\n",
|
|
" b = torch.zeros((1), requires_grad=True)\n",
|
|
" net, loss = lambda X: d2l.linreg(X, w, b), d2l.squared_loss\n",
|
|
" # 训练模型\n",
|
|
" animator = d2l.Animator(xlabel='epoch', ylabel='loss',\n",
|
|
" xlim=[0, num_epochs], ylim=[0.22, 0.35])\n",
|
|
" n, timer = 0, d2l.Timer()\n",
|
|
" for _ in range(num_epochs):\n",
|
|
" for X, y in data_iter:\n",
|
|
" l = loss(net(X), y).mean()\n",
|
|
" l.backward()\n",
|
|
" trainer_fn([w, b], states, hyperparams)\n",
|
|
" n += X.shape[0]\n",
|
|
" if n % 200 == 0:\n",
|
|
" timer.stop()\n",
|
|
" animator.add(n/X.shape[0]/len(data_iter),\n",
|
|
" (d2l.evaluate_loss(net, data_iter, loss),))\n",
|
|
" timer.start()\n",
|
|
" print(f'loss: {animator.Y[0][-1]:.3f}, {timer.avg():.3f} sec/epoch')\n",
|
|
" return timer.cumsum(), animator.Y[0]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6082ed33",
|
|
"metadata": {
|
|
"origin_pos": 40
|
|
},
|
|
"source": [
|
|
"让我们来看看批量梯度下降的优化是如何进行的。\n",
|
|
"这可以通过将小批量设置为1500（即样本总数）来实现。\n",
|
|
"因此，模型参数每个迭代轮数只迭代一次。\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "9d3c9c35",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:00:54.637080Z",
|
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"iopub.status.busy": "2023-08-18T07:00:54.636377Z",
|
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"iopub.status.idle": "2023-08-18T07:00:56.139533Z",
|
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"shell.execute_reply": "2023-08-18T07:00:56.138355Z"
|
|
},
|
|
"origin_pos": 41,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
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"outputs": [
|
|
{
|
|
"name": "stdout",
|
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"output_type": "stream",
|
|
"text": [
|
|
"loss: 0.243, 0.055 sec/epoch\n"
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]
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},
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"当批量大小为1时，优化使用的是随机梯度下降。\n",
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"现在我们可以比较前四个实验的时间与损失。\n",
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"可以看出，尽管在处理的样本数方面，随机梯度下降的收敛速度快于梯度下降，但与梯度下降相比，它需要更多的时间来达到同样的损失，因为逐个样本来计算梯度并不那么有效。\n",
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"小批量随机梯度下降能够平衡收敛速度和计算效率。\n",
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"d2l.set_figsize([6, 3])\n",
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|
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"source": [
|
|
"## 简洁实现\n",
|
|
"\n",
|
|
"下面用深度学习框架自带算法实现一个通用的训练函数，我们将在本章中其它小节使用它。\n"
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]
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"metadata": {
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"execution": {
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},
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"origin_pos": 52,
|
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"tab": [
|
|
"pytorch"
|
|
]
|
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},
|
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"outputs": [],
|
|
"source": [
|
|
"#@save\n",
|
|
"def train_concise_ch11(trainer_fn, hyperparams, data_iter, num_epochs=4):\n",
|
|
" # 初始化模型\n",
|
|
" net = nn.Sequential(nn.Linear(5, 1))\n",
|
|
" def init_weights(m):\n",
|
|
" if type(m) == nn.Linear:\n",
|
|
" torch.nn.init.normal_(m.weight, std=0.01)\n",
|
|
" net.apply(init_weights)\n",
|
|
"\n",
|
|
" optimizer = trainer_fn(net.parameters(), **hyperparams)\n",
|
|
" loss = nn.MSELoss(reduction='none')\n",
|
|
" animator = d2l.Animator(xlabel='epoch', ylabel='loss',\n",
|
|
" xlim=[0, num_epochs], ylim=[0.22, 0.35])\n",
|
|
" n, timer = 0, d2l.Timer()\n",
|
|
" for _ in range(num_epochs):\n",
|
|
" for X, y in data_iter:\n",
|
|
" optimizer.zero_grad()\n",
|
|
" out = net(X)\n",
|
|
" y = y.reshape(out.shape)\n",
|
|
" l = loss(out, y)\n",
|
|
" l.mean().backward()\n",
|
|
" optimizer.step()\n",
|
|
" n += X.shape[0]\n",
|
|
" if n % 200 == 0:\n",
|
|
" timer.stop()\n",
|
|
" # MSELoss计算平方误差时不带系数1/2\n",
|
|
" animator.add(n/X.shape[0]/len(data_iter),\n",
|
|
" (d2l.evaluate_loss(net, data_iter, loss) / 2,))\n",
|
|
" timer.start()\n",
|
|
" print(f'loss: {animator.Y[0][-1]:.3f}, {timer.avg():.3f} sec/epoch')"
|
|
]
|
|
},
|
|
{
|
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"cell_type": "markdown",
|
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"id": "973d2140",
|
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"metadata": {
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"origin_pos": 55
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},
|
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"source": [
|
|
"下面使用这个训练函数，复现之前的实验。\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"id": "c443d323",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T07:01:11.828129Z",
|
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"iopub.status.busy": "2023-08-18T07:01:11.827413Z",
|
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"iopub.status.idle": "2023-08-18T07:01:18.659993Z",
|
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"shell.execute_reply": "2023-08-18T07:01:18.658861Z"
|
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},
|
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"origin_pos": 57,
|
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"tab": [
|
|
"pytorch"
|
|
]
|
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},
|
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"outputs": [
|
|
{
|
|
"name": "stdout",
|
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"output_type": "stream",
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"text": [
|
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"loss: 0.243, 0.015 sec/epoch\n"
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]
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},
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"source": [
|
|
"data_iter, _ = get_data_ch11(10)\n",
|
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"trainer = torch.optim.SGD\n",
|
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"train_concise_ch11(trainer, {'lr': 0.01}, data_iter)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fd1152ec",
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"metadata": {
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"source": [
|
|
"## 小结\n",
|
|
"\n",
|
|
"* 由于减少了深度学习框架的额外开销，使用更好的内存定位以及CPU和GPU上的缓存，向量化使代码更加高效。\n",
|
|
"* 随机梯度下降的“统计效率”与大批量一次处理数据的“计算效率”之间存在权衡。小批量随机梯度下降提供了两全其美的答案：计算和统计效率。\n",
|
|
"* 在小批量随机梯度下降中，我们处理通过训练数据的随机排列获得的批量数据（即每个观测值只处理一次，但按随机顺序）。\n",
|
|
"* 在训练期间降低学习率有助于训练。\n",
|
|
"* 一般来说，小批量随机梯度下降比随机梯度下降和梯度下降的速度快，收敛风险较小。\n",
|
|
"\n",
|
|
"## 练习\n",
|
|
"\n",
|
|
"1. 修改批量大小和学习率，并观察目标函数值的下降率以及每个迭代轮数消耗的时间。\n",
|
|
"1. 将小批量随机梯度下降与实际从训练集中*取样替换*的变体进行比较。会看出什么？\n",
|
|
"1. 一个邪恶的精灵在没通知你的情况下复制了你的数据集（即每个观测发生两次，数据集增加到原始大小的两倍，但没有人告诉你）。随机梯度下降、小批量随机梯度下降和梯度下降的表现将如何变化？\n"
|
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]
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},
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"id": "0e60c65b",
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"origin_pos": 62,
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"tab": [
|
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"pytorch"
|
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]
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},
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"source": [
|
|
"[Discussions](https://discuss.d2l.ai/t/4325)\n"
|
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]
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}
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],
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